Turing degrees of reals of positive effective packing dimension
Information Processing Letters
K-Trivial Closed Sets and Continuous Functions
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
A Weakly 2-Random Set That Is Not Generalized Low
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Universal Recursively Enumerable Sets of Strings
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
Non-cupping, measure and computably enumerable splittings
Mathematical Structures in Computer Science
On universal computably enumerable prefix codes
Mathematical Structures in Computer Science
Superhighness and Strong Jump Traceability
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Chaitin Ω Numbers and Halting Problems
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Comparing notions of randomness
Theoretical Computer Science
Algorithmically independent sequences
Information and Computation
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
How powerful are integer-valued martingales?
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Counting the changes of random Δ20 sets
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Simplicity via provability for universal prefix-free Turing machines
Theoretical Computer Science
Representation of left-computable ε-random reals
Journal of Computer and System Sciences
Universal recursively enumerable sets of strings
Theoretical Computer Science
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Kolmogorov complexity of initial segments of sequences and arithmetical definability
Theoretical Computer Science
Theoretical Computer Science
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Three theorems on n-REA degrees: proof-readers and verifiers
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
Towards an axiomatic system for Kolmogorov complexity
CiE'11 Proceedings of the 7th conference on Models of computation in context: computability in Europe
On the number of infinite sequences with trivial initial segment complexity
Theoretical Computer Science
A Chaitin $$\Upomega$$ number based on compressible strings
Natural Computing: an international journal
Effectively approximating measurable sets by open sets
Theoretical Computer Science
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
Phase transition between unidirectionality and bidirectionality
WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
A K-trivial set which is not jump traceable at certain orders
Information Processing Letters
Arithmetic complexity via effective names for random sequences
ACM Transactions on Computational Logic (TOCL)
Process and truth-table characterisations of randomness
Theoretical Computer Science
Von Neumann's Biased Coin Revisited
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Turing's normal numbers: towards randomness
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Randomness, computation and mathematics
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Effective strong nullness and effectively closed sets
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
How much randomness is needed for statistics?
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Relative randomness for martin-löf random sets
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Strong reductions in effective randomness
Theoretical Computer Science
Lowness for bounded randomness
Theoretical Computer Science
IDA'12 Proceedings of the 11th international conference on Advances in Intelligent Data Analysis
Mathematical Structures in Computer Science
Analogues of Chaitin's Omega in the computably enumerable sets
Information Processing Letters
Traces, traceability, and lattices of traces under the set theoretic inclusion
Archive for Mathematical Logic
Universal computably enumerable sets and initial segment prefix-free complexity
Information and Computation
Initial segment complexities of randomness notions
Information and Computation
Archive for Mathematical Logic
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The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. Covering the basics as well as recent research results, this book provides a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.